Tidal effects on magnetic gyration of a charged particle in Fermi coordinates

TL;DR

This paper investigates how tidal forces near a Schwarzschild black hole affect the magnetic gyration of a charged particle, revealing velocity-dependent disruption behaviors and implications for stellar collapse.

Contribution

It introduces a model analyzing the impact of tidal forces on charged particle orbits in Fermi coordinates near a black hole, highlighting velocity effects on disruption.

Findings

Disruption velocity depends on initial circular velocity, with a critical point at ~0.7c.

Rapidly rotating stars may experience different tidal disruption than non-relativistic stars.

Orbit collapse is slow, allowing particles to escape Fermi coordinates after disruption.

Abstract

We examine the gyration motion of a charged particle, viewed from a reference observer falling along the Z axis into a Schwarzschild black hole. It is assumed that the magnetic field is constant and uniform along the Z axis, and that the particle has a circular orbit in the X-Y plane far from the gravitational source. When the particle as well as the reference observer approaches the black hole, its orbit is disrupted by the tidal force. The final plunging velocity increases in the non-relativistic case, but decreases if the initial circular velocity exceeds a critical value, which is approximately 0.7c. This toy model suggests that disruption of a rapidly rotating star due to a velocity-dependent tidal force may be quite different from that of a non-relativistic star. The model also suggested that collapse of the orbit after the disruption is slow in general, so that the particle subsequently escapes outside the valid Fermi coordinates.